Sound Pressure Level Calculator
Enter RMS sound pressure to compute SPL=20·log₁₀(p/p₀) in dB, sound intensity I=p²/(ρc) and SIL=10·log₁₀(I/I₀). p=0.02 Pa (talk) → 60 dB; p=1 Pa → 94 dB; p=200 Pa (jet) → 140 dB (pain).
Input Data
Results
At a glance:Sound pressure level (SPL): a logarithmic (decibel) measure of sound pressure, SPL=20·log₁₀(p/p₀), where p is the RMS sound pressure (Pa) and p₀=20 μPa=2×10⁻⁵ Pa the reference (air, 1 kHz hearing threshold). Every +6 dB doubles the pressure, every +20 dB multiplies it 10×. Sound intensity I=p²/(ρc) (W/m²), ρc≈412 kg/(m²·s) the 20°C air characteristic impedance. SIL=10·log₁₀(I/I₀), I₀=10⁻¹² W/m² the reference intensity. In air SPL=SIL numerically (4×10⁻¹⁰ W/m²=0 dB). History: Bell defined the decibel in the 1920s telephone engineering; the Weber–Fechner law (sensation ∝ log stimulus) underlies the logarithmic scale. Classic example: p=1 Pa, p₀=20 μPa → SPL=20·log(50000)=94 dB; p=20 μPa → 0 dB (threshold); p=200 Pa → 140 dB (pain). Applications: (1) noise measurement — sound-level meters; (2) hearing protection — factories, airports; (3) audio engineering — recording, PA; (4) environmental assessment — road and building noise; (5) medical ultrasound — pressure safety standards.
Formula
SPL = 20·log₁₀(p / p₀)
Reference p₀ = 20μPa = 2×10⁻⁵ Pa (air)
Intensity: I = p² / (ρ·c)
SIL = 10·log₁₀(I / I₀), I₀=10⁻¹² W/m²
Pressure ×2 → +6 dB; ×10 → +20 dB
$$\text{SPL} = 20\log_{10}\!\frac{p}{p_0}, \quad p_0 = 2\times 10^{-5}\,\text{Pa}, \quad I = \frac{p^2}{\rho c}, \quad \text{SIL} = 10\log_{10}\!\frac{I}{I_0}$$How to Use
- Enter sound pressure p (Pa) and reference p₀ (Pa, default 20 μPa air).
- The tool gives SPL=20·log₁₀(p/p₀), intensity I=p²/(ρc) and SIL.
Case Studies
Noise limits and hearing protection
Normal talk ~60 dB (p≈0.02 Pa); busy road ~80 dB; jet takeoff ~140 dB (pain).
HK noise ordinance: construction >90 dB(A) at boundary needs mitigation; workplaces cap 85 dB(A) 8-hour.
Each 3 dB halves safe exposure time — ear protection is mandatory above limits.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.